From the mixture multigroup SEM framework, the novel method Mixture Multilevel SEM (MixML-SEM) was developed, where random effects capture differences in measurement parameters across the groups, so that they don’t affect the clustering. In an extensive simulation study, it was compared to multilevel SEM (ML-SEM), which is, for many researchers, the preferred method for comparing structural relations (i.e. regression relations among latent variables or latent processes) across many groups. We showed that ML-SEM produces group-specific structural relations that are incorrectly estimated for smaller groups, and cumbersome to compare. In contrast, MixML-SEM provides accurate estimates of the structural relations of interest and an efficient comparison of groups in terms of structural relations by assigning groups with the same structural relations to the same cluster. In this way, one only needs to compare the relations between the clusters of groups (rather than between individual groups). Finding a clustering of groups specifically focused on the structural relations, and unaffected by differences in measurement, was a key objective of the project, which is thus achieved.
A second method of the framework, Mixture Multigroup Bayesian SEM (MixMG-BSEM), was also developed, where small differences in measurement parameters are captured by small-variance priors around the measurement parameters. A good performance was found in a large simulation study, which also showed that MixMG-BSEM is quite robust to the choice of the prior variances.
In order to accommodate mixture multigroup SEM methods with an exploratory measurement model (where it is unknown beforehand which items are measuring which latent variables), we are evaluating how structural relations should be compared across groups when the measurement model is exploratory.
Users have to specify the number of clusters for the data set at hand (model selection). In an extensive simulation study, we confirmed that existing techniques for selecting the number of clusters succeed in correctly identifying the number of clusters for MixML-SEM. These results generalize to other methods of the framework.
